Graffiti Conjecture 806

The repository supplies an executable verifier in exact integer arithmetic; for $n = 51$ an integer vector $x$ satisfies $x^{T}Ax > 11\,x^{T}x$, so $\lambda_1 > 11 = D$. The deficit $\lambda_1(n) - D(n)$ grows through $n = 5000$ in the repository's computations, but no asymptotic theorem proving divergence is claimed, so "false for every constant $C$" is a computed pattern, not a proved one. One anomaly, which the repository records itself: $n = 51$ lies inside the range Graffiti is said to have tested when it made the conjecture.

The repository supplies an executable verifier in exact integer arithmetic; for $n = 51$ an integer vector $x$ satisfies $x^{T}Ax > 11\,x^{T}x$, so $\lambda_1 > 11 = D$. The deficit $\lambda_1(n) - D(n)$ grows through $n = 5000$ in the repository's computations, but no asymptotic theorem proving divergence is claimed, so "false for every constant $C$" is a computed pattern, not a proved one. One anomaly, which the repository records itself: $n = 51$ lies inside the range Graffiti is said to have tested when it made the conjecture.